Two-Phase Electrochemical Lithiation in Amorphous SiliconJiang Wei Wang,†,⊥ Yu He,‡,⊥ Feifei Fan,§ Xiao Hua Liu,∥ Shuman Xia,§ Yang Liu,∥ C. Thomas Harris,∥

Hong Li,*,‡ Jian Yu Huang,∥ Scott X. Mao,*,† and Ting Zhu*,§

†Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, UnitedStates‡Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190,People’s Republic of China§Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States∥Center for Integrated Nanotechnologies (CINT), Sandia National Laboratories, Albuquerque, New Mexico 87185, United States

*S Supporting Information

ABSTRACT: Lithium-ion batteries have revolutionized portableelectronics and will be a key to electrifying transport vehicles anddelivering renewable electricity. Amorphous silicon (a-Si) is beingintensively studied as a high-capacity anode material for next-generation lithium-ion batteries. Its lithiation has been widelythought to occur through a single-phase mechanism with gentle Liprofiles, thus offering a significant potential for mitigatingpulverization and capacity fade. Here, we discover a surprising two-phase process of electrochemical lithiation in a-Si by using in situtransmission electron microscopy. The lithiation occurs by the movement of a sharp phase boundary between the a-Si reactantand an amorphous LixSi (a-LixSi, x ∼ 2.5) product. Such a striking amorphous−amorphous interface exists until the remaining a-Si is consumed. Then a second step of lithiation sets in without a visible interface, resulting in the final product of a-LixSi (x ∼3.75). We show that the two-phase lithiation can be the fundamental mechanism underpinning the anomalous morphologicalchange of microfabricated a-Si electrodes, i.e., from a disk shape to a dome shape. Our results represent a significant step towardthe understanding of the electrochemically driven reaction and degradation in amorphous materials, which is critical to thedevelopment of microstructurally stable electrodes for high-performance lithium-ion batteries.

KEYWORDS: Amorphous silicon, two-phase lithiation, amorphous−amorphous interface, lithium-ion battery,in situ transmission electron microscopy

Silicon is an attractive high-capacity anode material for Li-ion batteries.1−7 However, insertion of Li into Si causes

large volume expansion of ∼280% at the full capacity (Li3.75Si)at room temperature. The issue of volume expansion isparticularly significant in Si electrodes that have been oftenfabricated from crystalline Si (c-Si). This is because lithiation ofc-Si occurs through a two-phase mechanism, i.e., growth ofamorphous LixSi (a-LixSi, x ∼ 3.75) separated from c-Si by asharp phase boundary.8−12 A large change of Li concentrationacross this amorphous−crystalline interface (ACI) of about 1nm in width can cause drastically inhomogeneous volumeexpansion, leading to high stress, pulverization, and capacityloss.8,13−16

To mitigate the degradation associated with the two-phaselithiation in c-Si, considerable efforts have been devoted to itsamorphous counterpart,17−23 which is intuitively thought toeliminate two-phase regions, resulting in a continuous Lireaction and homogeneous volume expansion. However,whether lithiation of amorphous Si (a-Si) occurs by a single-phase or two-phase mechanism remains unclear.24−27 A furtherinterest in this question arises from the experiment reported in

this paper which reveals anomalous shape changes during theelectrochemical lithiation of patterned a-Si disk electrodes.To clearly resolve how a-Si is lithiated, we conduct in situ

experiment of electrochemical lithiation inside a transmissionelectron microscope (TEM). Real-time visualization of the firstlithiation process directly reveals a two-phase mechanism thatoccurs by movement of a sharp phase boundary between the a-Si reactant and an a-LixSi (x ∼ 2.5) product. It is unexpected toobserve such an amorphous−amorphous interface (AAI),which has been rarely seen in the literature of solid-statephase transformations.28−31 Unique to the lithiation of a-Si,there exists an abrupt change of Li concentration across thephase boundary that renders a marked contrast in electrontransparency between the two coexisting amorphous phases,thereby facilitating the discovery of the AAI through in situTEM. Upon the completion of two-phase lithiation, a secondstep of lithiation occurs in a-LixSi (x ∼ 2.5) without a visible

Received: November 28, 2012Revised: January 12, 2013Published: January 16, 2013

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interface, resulting in the final product of a-LixSi (x ∼ 3.75)with a total volume expansion of about 280%. Nevertheless, thepredominance of two-phase lithiation appears to be the key toanomalous shape growth in microfabricated a-Si electrodes, asshown by our chemomechanical modeling.Results and Discussion. Anomalous Growth of a-Si Disk

Electrodes. Figure 1 shows the anomalous shape changes of apatterned a-Si electrode during electrochemical lithiation. Theas-fabricated electrode consisted of an array of equally spacedcircular microdisks on a titanium (Ti)-coated quartz substrate,as revealed by the scanning electron microscope (SEM) imagein Figure 1a. Each of the disks had a thickness of 500 nm and adiameter of 5 μm, and the distance between the neighboringdisks was also 5 μm. The Raman spectra indicate that as-prepared Si disks were amorphous (Figure S1). Electrochemicallithiation was conducted with the patterned a-Si electrode, andSEM images were taken to follow the morphological evolutionduring various stages of lithiation (Figures 1b,c). Figure 1dshows the normalized voltage profile during the first lithiation,in which the red dots marked as “a” through “c” correspond tothe SEM images shown in Figures 1a−c, respectively. Thegrowth of the a-Si disk electrodes upon lithiation was highlyanisotropic, with the vertical expansion dominating the lateralone. The most striking shape change was the anomalousnonuniform expansion; namely, the vertical expansion of thedisk electrode increased markedly with decreasing radialdistance, resulting in a final dome shape at the conclusion oflithiation. From both SEM imaging and atomic forcemicroscope (AFM) measurement, we estimate the volumeexpansion around 280%, confirming an approximately fulllithiation to a-Li3.75Si (He et al.

21). In addition, the base of thelithiated disk electrode expanded by ∼20% in the radialdirection, which is suggestive of the occurrence of interfacialsliding or plastic flow in the metallic substrate foraccommodating the radial growth.22,23

Two-Phase Mechanism in a-Si Revealed by in SituElectrochemical Lithiation. To understand the formation ofthe dome shape, we directly visualized how a-Si was lithiatedwith in situ electrochemical lithiation experiments inside aTEM. As schematically shown in Figure S2, a nanobattery wasconstructed in the half-cell configuration.32,33 The working

electrode was an individual carbon nanofiber coated with an a-Si surface layer, denoted as a-Si/CNF. Figures 2a−c show theTEM image and electron diffraction pattern of a-Si/CNFbefore lithiation. The CNF was hollow, with both the outer andinner surfaces covered with a-Si (Figure 2a). Figure 2b shows ahigh-magnification TEM image of the surface a-Si layer beforelithiation. This a-Si layer was disordered, with a thickness ofabout 20 nm. On the surface of the a-Si layer, a thin layer ofamorphous carbon (3 nm thick) was coated to serve as a fastpath for Li+ ion and electron transport in the longitudinaldirection of the system. Beneath the a-Si layer, the CNFexhibited a pattern of layered graphitic sheets. The electrondiffraction pattern of a-Si/CNF (Figure 2c) confirms that the Silayer is amorphous. Upon lithiation, Li+ ions first diffused alongthe fast paths, i.e., the surface of a-Si and the interface betweena-Si and CNF, and then diffused into the bulk of the a-Si layeralong the radial direction. This sequential process resulted in asandwiched mode of lithiation in a-Si,27 as shown in Figure S3.To highlight the essential physical process, we hereafter focuson the in situ high-resolution TEM characterization of two-phase lithiation in the surface a-Si layer.Figures 2d−f and the video in the Supporting Information

show the dynamic propagation of an individual AAI, whichinitiated near the surface and moved toward the center of CNF.The pristine a-Si surface layer on the CNF was initially about21 nm (Figure 2d). Upon lithiation, Li+ ions consumed Siatoms by forming an a-LixSi alloy, and a sharp phase boundaryformed between the a-Si and a-LixSi layer. As the phaseboundary propagated, the lithiated layer was markedlythickened and the a-Si layer was gradually depleted (Figures2e,f). Figure 2g shows the thickness versus time in a-Si and a-LixSi. The velocity of the AAI is approximately constant (0.06nm/s), which indicates that the lithiation reaction at the phaseboundary is the rate-limiting step.34 Assuming cylindricalsymmetry, we estimate the volume increase in the a-LixSilayer relative to its pristine state, as shown in Figure 2h. Thisresult, along with in situ testing of several other a-Si/CNFs(Figures S4a−c and S5a−c), suggests the average value of x tobe about 2.5 in the a-LixSi phase (corresponding to volumeexpansion ∼170%, ref 35). While the TEM contrast wasinadequate for resolving the Li distribution in the a-LixSi layer,

Figure 1. Anomalous shape growth of electrochemically lithiated amorphous Si electrodes.21 (a) SEM image of as-fabricated a-Si disk electrodes. (b)An intermediate state of a representative disk electrode during electrochemical lithiation. (c) A fully lithiated disk electrode exhibiting the domelikeshape. (d) Normalized voltage versus lithiation capacity. A full lithiation corresponds to the formation of a-Li3.75Si. Red dots indicate the statesshown in the SEM images of (a−c).

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we performed the digital image correlation (DIC) analysis toquantitatively determine the spatial distribution of lithiation-induced strains from TEM images. As detailed in theSupporting Information, our DIC results show that (1) theLi diffusion-induced strain is negligibly small in the a-LixSi layeras the a-Si/a-LixSi phase boundary moves and (2) the localphase-transformation-induced strain is about 160% in theregion swept by the a-Si/a-LixSi phase boundary. These resultsindicate that the lithiation-induced expansion dominantlyoccurs at the a-Si/a-LixSi phase boundary, and the Liconcentration gradient is negligibly small in the lithiated layerof a-LixSi (x ∼ 2.5). It is worth noting that the localizedlithiation could be accelerated due to the high dosage rate ofelectron beam exposure required by high-resolution TEMimaging (Figure S6). This is in contrast with the extendedlithiation through the propagation of a long and straight phaseboundary under the beam-blank or low-resolution imagingconditions. Nevertheless, the observation of sharp phaseboundaries remained the same and reproducible in all the

TEM experiments (Figure 2 and Figures S3−S6), clearlyshowing that the two-phase mechanism dominates in theelectrochemical lithiation of a-Si. In addition, in situ TEMobservation shows that the two-phase boundary exists until theremaining a-Si is consumed. This is followed by a second stepof lithiation in a-LixSi (x ∼ 2.5) without a visible interface,resulting in the final product of a-LixSi (x ∼ 3.75) with a totalvolume expansion of ∼280%, as shown in Figures S4d and S5d.This step of lithiation proceeded extremely fast, and we werenot able to acquire a series of high-quality TEM images. Hence,unlike the first step of lithiation, the strain field could not bequantified by the DIC analysis for determining Li distributions.Future studies are needed with a better control of the second-step lithiation in a-Si in order to clarify whether it occurs by asingle-phase or two-phase reaction.The above in situ TEM experiment reveals an unexpected

two-phase process of electrochemical lithiation in a-Si. Tounderstand why the two-phase mechanism dominates thesingle-phase one in the first step of lithiation, we recall that the

Figure 2. A sharp phase boundary observed during in situ electrochemical lithiation of amorphous Si coated on a carbon nanofiber. (a−c) Pristine a-Si/CNF. The CNF is hollow, with both the outer and inner surfaces covered with a-Si. The a-Si coating layer is about 20 nm thick, and it is coveredwith an amorphous carbon layer of 3 nm thick. The high-resolution TEM image (b) and electron diffraction pattern (c) indicate that the Si coatinglayer is amorphous. The yellow arrows in (b) indicate the interface between a-Si and CNF. (d−f) Time-elapse high-resolution TEM images showingthe migration of a phase boundary between a-Si and a-LixSi. The a-LixSi layer in (f) grew to 19 nm thick and had a lighter contrast than theunderneath a-Si, whose thickness decreased from 21 nm (shown in (d)) to 13 nm. (g) Thickness versus time in a-Si and a-LixSi, and (h) theassociated volume increase in the a-LixSi layer.

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linear time dependence of thickening of a-LixSi (Figure 2g)indicates that the reaction at the amorphous−amorphousinterface is the rate-limiting step. The disruption of a covalentSi network, either crystalline or amorphous, is generally knownto be difficult. This is because of the strong covalent Si−Sibonding; e.g., the energy needed to remove a Si atom from thec-Si surface has been measured to be a large fraction of theformation energy of a vacancy (2.4−3.5 eV, ref 36), resulting ina low rate of Si dissociation from the Si network at roomtemperature. Incidentally, our recent in situ high-resolutionTEM experiment has revealed a two-phase lithiation mecha-nism of c-Si to a-LixSi through the movement of a sharpamorphous−crystalline interface (Figure 3a), facilitated bylayer-by-layer ledge flow at the c-Si surface.11 While the atomicstructure of a-Si lacks the long-range order, it consists of acontinuous random network of Si atoms. The local bondingenvironment in a-Si is similar to that of c-Si (Figures 3b,e), in

the sense that both a-Si and c-Si involve the strong, directionalSi bonding with a small number of miscoordinated/over-coordinated defects. As a result, in both cases the local Liconcentration near the phase boundary should be high in theLi-rich a-LixSi phase, so as to facilitate an interfacial process ofseveral Li atoms enclosing a single Si or a Si−Si pair at thesurface of c-Si or a-Si,37,38 as illustrated in Figures 3c,f. Theprevious study of silicide formation indicates that a group ofmetallic atoms (Li in this case) can collectively weaken the Si−Si covalent bonding by electron transfer.36 Hence, the Li“flocking” at the amorphous−amorphous phase boundary isexpected to lead to easy dissociation of the Si atom from thecovalently bonded a-Si (Figure 3f), facilitating the lithiationprocess at room temperature.On the basis of the newly discovered two-phase lithiation in

a-Si, our continuum chemomechanical simulation readilyproduced a dome shape during lithiation of the a-Si disk

Figure 3. Comparison of the two-phase lithiation mechanism in c-Si and a-Si. (a) A high-resolution TEM image showing a sharp phase boundarybetween the reactant of c-Si and the product of a-LixSi.

11 (b) A snapshot from molecular dynamics simulation showing the atomic structures near theamorphous−crystal phase boundary.11 The Li concentration is locally high near the surface of c-Si (red) and a group of Li atoms (green) collectivelyweaken the strong Si−Si covalent bonding, thereby facilitating the dissolution of Si atom from c-Si surface, as schematically shown in (c). (d) A high-resolution TEM image showing a sharp phase boundary between a-Si and a-LixSi (x ∼ 2.5). (e) A snapshot from molecular dynamics simulationshowing the atomic structures near the amorphous−amorphous interface. The a-Si consists of a continuous random network of Si atoms. Similar to(b), the Li concentration is locally high near the surface of a-Si. (f) Schematics showing the proposed mechanism of dissolution of Si atoms from thea-Si surface into a-LixSi alloy.

Figure 4. Chemomechanical simulation of lithiation-induced morphological evolution in an a-Si disk electrode. (a−c) The first step of two-phaselithiation to form a-Li2.5Si, showing both the Li profile and shape growth: (a) a pristine a-Si electrode on a Ti substrate; (b) an intermediate state,showing the simulated amorphous−amorphous interface (AAI); and (c) a state close to the final a-Li2.5Si. A drastic change of Li concentrationoccurs across the sharp AAI between a-Si and a-Li2.5Si. Note that the remaining a-Si electrode undergoes a marked shrinkage in the radial direction.Contour indicates the normalized Li concentration of c; a-Si and a-Li2.5Si correspond to c = 0 and 0.67, respectively. (d, e) The second step of single-phase lithiation to form a-Li3.75Si: (d) an intermediate state, showing the smooth and gentle Li distribution; and (e) the final state of a-Li3.75Si. Todisplay the gradual change of Li concentrations in (d, e), a color map different from (a−c) is used, with a-Li3.7.5Si corresponding to c = 1.

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electrode shown in Figure 1c. Figures 4a−c show the snapshotsof simulated Li distributions and associated shape changes in adisk electrode undergoing two-phase lithiation. These resultssuggest two dominant factors that control the dome shapegrowth. First, the sharp phase boundary between a-Si and a-LixSi (x ∼ 2.5) is responsible for anisotropic swelling byeffectively promoting the vertical expansion while suppressingthe lateral expansion. This arises from the drastic change of Liconcentration across the phase boundary. That is, in order tominimize the strain mismatch between the unlithiated andlithiated phase, the lithiation strain occurring at the phaseboundary tends to align with the local normal direction of thephase boundary. Note that the disk electrode in our experimentfeatures a large aspect ratio between diameter and height, sothat the majority of the phase boundary is parallel to thesubstrate, as shown in Figure 4b. As a result, the lithiation-induced expansion occurs dominantly in the vertical direction.In addition, assuming a finite shear strength against interfacialsliding between the disk electrode and substrate,22,23 oursimulations capture the radial expansion of about 20%, asmeasured from the experiment.Second, the decreasing diameter of the unlithiated a-Si disk

dictates the dome shape growth. Figures 4a−c show that aslithiation proceeds, the diameter of the unlithiated a-Si diskdecreases, due to simultaneous in-flow of Li from both the topand side surfaces. This leads to a progressive decrease of thearea of the phase boundary that is parallel to the substrate. Thevertical expansion occurs mostly at this part of phase boundarywith reducing area and thus gradually focuses onto the center ofthe disk electrode. As a result, the dome shape develops,featuring a markedly increased vertical expansion withdecreasing radial distance to the disk center. It should benoted that the second step of lithiation, either by a single-phaseor two-phase reaction, will not qualitatively change the finalresult of formation of a dome shape in the lithiated diskelectrode. For example, we simulated the second step oflithiation from a-Li2.5Si to a-Li3.75Si by assuming a single-phasereaction with gentle Li profiles. As shown in Figure 4d,e, theelectrode with an already dome shape further expands in anearly self-similar manner, giving a final volume expansion of∼280% at the conclusion of lithiation to a-Li3.75Si.Finally, we note that while the anomalous shape growth in

the microfabricated a-Si electrode is rationalized in terms of theeffects of two-phase lithiation, its origin requires further studyregarding the influence of the lithiation stress on Li diffusion,reaction, and deformation. At this point we cannot exclude thepossibility that the dome shape would arise from the single-phase lithiation with gentle Li profiles, owing to the volumeexpansion mediated by the lithiation stress. However, we notethat the redox peaks can be clearly seen in the cyclicvoltammogram or dQ/dV (where Q is charge and V is voltage)curve for the a-Si thin film electrode (Figure S7). Similar redoxpeaks in a-Si are also reported in the literature.39,40 The redoxpeak has been often correlated to the two-phase reaction. Thefirst redox peak in Figure S7 likely results from the two-phasereaction between a-Si and a-LixSi (x ∼ 2.5), and the secondpeak could be related to the transition from a-Li2.5Si to a-Li3.75Si. The redox peaks therefore lend a support to the two-phase reaction mechanism. Moreover, our chemo-mechanicalsimulations indicate that the stress effect on shape growthshould be secondary compared to the two-phase mechanism oflithiation (Figure S8 shows a typical simulation result of single-phase lithiation). Nevertheless, the experiment of micro-

fabricated a-Si disk electrodes motivated the in situ TEMstudy, leading to a discovery of the two-phase electrochemicallithiation in amorphous electrodes.

Conclusions. We have discovered an unexpected two-phaselithiation mechanism in amorphous silicon through in situ TEMexperiment. Such lithiation mechanism is in stark contrast tothe widely believed single-phase mechanism in amorphousmetals and alloys. The occurrence of a sharp amorphous−amorphous interface during electrochemical lithiation isattributed to the need for a high local Li concentration at thephase boundary so as for it to break the Si atom away from thecovalently bonded a-Si. The two-phase lithiation can cause theanomalous morphological change of microfabricated amor-phous silicon electrodes. Our work represents an importantadvance in the fundamental understanding of the workingmechanisms of the high-capacity, amorphous electrodes inlithium-ion batteries.41,42 Broadly, the demonstrated capabilityof in situ visualization of the amorphous−amorphous phaseboundary opens new opportunities for the study of polya-morphism in amorphous materials.28−31

Methods. Ex Situ Electrochemical Test of the Patterned a-Si Electrode. An array of a-Si disk electrodes was made from auniform a-Si thin film on a Ti-coated quartz substrate with theoptical lithography and reactive ion etching (RIE) techniques,as described in detail in our previous work.21 The a-Si thin filmwas deposited by radio-frequency sputtering of a pure Si(>99.999%) target with the sputtering power of 60 W. Beforedeposition, the vacuum chamber was evacuated to a pressure of5.0 × 10−5 Pa and then was kept at 4 mTorr under high-purityargon (99.999%) ambient during deposition. The substrate was500 nm thick Ti deposited on quartz by dc magnetronsputtering of a pure Ti (>99.999%) target. The S1813 (ShipleyCo.) photoresist was spin-coated onto the as-prepared a-Sielectrode and prebaked at 115 °C for 60 s. The exposure wascarried out by an ultraviolet mask aligner system (KarlSussMA6, Germany). A PlasmaLab 80 plus RIE system(Oxford Instruments Company, UK) was used to transfer theresist patterns to the Si film. Reactive etching was conducted inSF6−O2 plasmon containing 30 standard cubic centimeter(sccm) SF6 and 5 sccm O2 at 100 mTorr for 2 min at 200 Wradio-frequency power. The as-prepared, patterned a-Sielectrode was analyzed with Raman spectroscopy with aRenishaw 1000NR spectrometer using an argon ion laser(wavelength λ = 514 nm). Spectra were collected in thewavenumber range of 200−1000 cm−1 with a resolution of 1cm−1.To conduct the electrochemical test, a two-electrode cell was

constructed with the patterned a-Si electrode as the workingelectrode and a Li foil as the counter electrode. The electrolytewas 1 M LiPF6 dissolved in ethylene carbonate and dimethylcarbonate with a volumetric ratio of 1:1 (Shanghai Topsol Ltd.,H2O < 10 ppm). The cell was discharged at a constant currentdensity of 5 μA cm−2. Ex situ AFM experiments wereperformed using an AFM workstation (Nano Scope IIIa,Bruker AXS) housed in an argon-purged glovebag. Contactmode was used in these ex situ AFM experiments. The AFMprobe used to image the surface was silicon nitride Veeco probe(OTR8-35). The sample was opened in the glovebag withoutexposure to air. Ex situ SEM experiments were performed by aHitachi-4800 microscope equipped with a sample transfer box,which permitted the transfer of air-sensitive samples from theglovebox into the SEM vacuum chamber without exposure toair. Before fixing the sample to the SEM holder, each electrode

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was washed with anhydrous dimethyl carbonate and dried inthe vacuum chamber in the glovebox.In Situ Electrochemical Test of a-Si. The a-Si/CNF

composite samples were prepared by coating a-Si onto CNFswith the chemical vapor deposition method (Applied SciencesInc.). The a-Si coating was about 20 nm. In a typical in situTEM experiment of electrochemical lithiation, the a-Si/CNFcomposite nanowires were glued to an aluminum (Al) rod withconductive silver epoxy, which served as the working electrode.Fresh Li metal was scratched off from a freshly cut surface ofbulk Li with a tungsten (W) rod in a glovebox filled withhelium (H2O and O2 concentration below 1 ppm), whichserved as the counter electrode and Li source. The twoelectrodes were mounted onto a Nanofactory TEM−scanningtunneling microscopy (STM) holder in a glovebox, which wastransferred with a sealed plastic bag filled with dry helium andloaded into the TEM column. The Li metal was exposed to theair for about 2−5 s during the holder loading process. A nativeLi2O layer was formed on the surface of Li metal, which servedas the solid-state electrolyte to only conduct Li+ ions. Inside theTEM, the Li2O/Li terminal was driven by a piezo positioner totouch the a-Si/CNF-Al terminal. Once the contact wasestablished, a negative bias (such as −2 V) was applied tothe a-Si/CNF electrode to initiate the electrochemicallithiation. Both beam blank and in situ experiments wereconducted to observe phase boundaries between the a-Sireactant and the a-LixSi product created during lithiation.Modeling. We first simulate the two-phase lithiation that

results in a-Li2.5Si. The evolution of phase and microstructure ismodeled by the nonlinear diffusion of Li, as described in detailin our recent work.8,13 In finite element simulations of Lidiffusion, the disk electrode is initially pristine and subjected toa constant Li flux I0 at the surface. The normalized Liconcentration behind the reaction front can quickly attain thehigh value (around c = 0.67, corresponding to a-Li2.5Si), whilethat ahead of the front remains nearly zero. This produces asharp reaction front, consistent with the experiment observa-tion. To describe the lithiation-induced deformation, we adoptan elastic and perfectly plastic model.8,13 The total strain rate,ε̇ij, is a sum of three contributions: εi̇j = ε̇ij

c + ε̇ije + ε̇ij

p. Here, εi̇je

and ε̇ijp denote the elastic and plastic strain rate, respectively; εi̇j

c

denotes the chemical strain rate caused by lithiation and isproportional to the rate of the normalized Li concentration, c.̇That is, ε̇ij

c = βijc,̇ where βij is the coefficient of lithiation-inducedvolume expansion. We assume that the outer surface of the diskelectrode is traction free, and the interface shear strength isconstant between the electrode and rigid substrate. We also testthe case of an elastic−perfectly plastic substrate with a perfectlybonded interface. The two interface conditions give nearlyindistinguishable results of the final dome shape, though thedetailed distributions of shear stresses near the interface areslightly different. The above diffusion and elastic−perfectlyplastic model is numerically implemented in the finite elementpackage ABAQUS.8,13 We also simulate the second step ofsingle-phase lithiation that forms a-Li3.75Si. In contrast to theaforementioned two-phase lithiation, we employ a constantdiffusivity, giving a gentle variation of Li profiles. The axis-symmetric condition is used to reduce the computational cost.We choose the volume expansion parameters to be β11 = β22 =β33 = 0.56, giving the total volume increase of 280% for a-Li3.75Si; the yield stress σY = 0.03E, where E is Young’smodulus, and Poisson’s ratio v = 0.3. To understand the atomicstructure near the phase boundary, we performed molecular

dynamics (MD) simulations by using the reactive force field.The detailed procedures have been described in our previouswork.11,35

■ ASSOCIATED CONTENT*S Supporting InformationA video from in situ high-resolution TEM imaging, showing thetwo-phase electrochemical lithiation of a-Si, along with thedigital image correlation (DIC) analysis of TEM images;additional figures of experiment and modeling. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: ting.zhu@me.gatech.edu (T.Z.); sxm2@pitt.edu(S.X.M.); hli@iphy.ac.cn (H.L.).Author Contributions⊥These authors contributed equally to this work.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank David Burton from Applied Sciences Inc. forproviding the a-Si/CNF samples. S.X.M. acknowledges theNSF grant CMMI 08010934 through University of Pittsburghand Sandia National Lab support. T.Z. acknowledges thesupport by the NSF Grant CMMI 1100205. This work wasperformed, in part, at the Center for Integrated Nano-technologies, a US Department of Energy, Office of BasicEnergy Sciences user facility. Sandia National Laboratories is amultiprogram laboratory managed and operated by SandiaCorporation, a wholly owned subsidiary of Lockheed MartinCompany, for the U.S. Department of Energy’s NationalNuclear Security Administration under Contract DE-AC04-94AL85000. The research done at the Institute of Physics,Chinese Academy of Sciences, is supported by CAS project(KJCX2-YW-W26) and 973 project (2012CB932900).

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Nano Letters Letter

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Nano Letters Letter

dx.doi.org/10.1021/nl304379k | Nano Lett. 2013, 13, 709−715715